3.
Example 1
Solve
Solution
Factorising
so either or
solution or
Example 3
Solve
Solution
Factorising
so either or
Example 2
Solve
Solution
Factorising
so either or
Example 4
Solve
Solution
Factorising
so there is only one (repeated) solution?
?
?
A quadratic equation is of the form
and can be solved easily if it factorises.
?
? ?
?
??
?
??
?
? ?
?

5.
?
There is a formula to solve the quadratic equation
The solution is given by
Example 1
Using the formula, solve the quadratic equation
Giving the solution correct to two decimal places.
Solution
Here so? ? ?
?
? ?
?
? ?
?
?
or
To 2 d.p. or
?
??? ?

11.
No. of solutions = 0
See previous Example 3
No. of solutions = 2
See previous Example 1
No. of solutions = 1
See previous Example 2
A quadratic equation can have 2,1 or 0 solutions.
The following graphs illustrate these graphically and show
how the number of solutions depend on the sign of
which is part of the quadratic formula.
?? ?

13.
This is and it occurs when
The formula for solving a quadratic equation comes from
completing the square.
Example
Express in the form when a, p and
q are real numbers.
Solution
? ? ?
? ?
So comparing
coefficients,
?
?
?
?
?
?Thus
Extension
What is the minimum value of ?
??